Can I upload all data at once in No Man's Sky?

No, there is no way to upload multiple discoveries at a time, unfortunately. There is an official blog post which states that they plan to keep updating the game after release though, so hopefully they will add that feature at some point in the future.

Yes, you can. It was added in a free patch.

Go to the Menu, Discoveries.

When not on a planet (in space somewhere) you can select the "Upload All" (up arrow) in the bottom left of the screen.

If on a planet, the Discoveries screen shows your current system. Go up a menu from there (right-click on PC) to the Visited Systems screen, and you can use the Upload All button.